What is the proper way to convert a digital picture file, out of a digital camera, from the RGB to CMYK so a print-shop can use that file in a color flyer, pamphlet, business card, magazine, etc? (Not for photo-prints on chemical-sensitive paper)
There is no "correct" way to do it. There are many, many different ways and all of them are equally correct. Are you looking to reduce it to spot color or is it full color printing? Does the resolution or color depth of their printing process require dithering? These all matter greatly for proper selection of how to convert the image.
If it is truely full color CMYK printing, it is simply a matter of opening it up in Photoshop and changing the color space to CMYK. (Under the Image menu if memory serves) Photoshop will find the nearest match and try to approximate (your display is RGB, so it won't be exact) the final color for you. You can then make adjustments as necessary to the image before saving it for print.
If it isn't full color CMYK with a comparable color space to your image, then things become considerably more challenging, however without more detail about the process you need there is too much to cover here.